Sigma-term form factor of the nucleon in the large-Nclimit

Abstract

The scalar isoscalar form factor $\ensuremath{\sigma}(t)$ of the nucleon is calculated in the limit of a large number of colors in the framework of the chiral quark-soliton model. The calculation is free of adjustable parameters and based on an approximation justified by the small packing fraction of instantons in the QCD vacuum model, from which the chiral quark-soliton model was derived. The result for $\ensuremath{\sigma}(t)$ reproduces all features of the form factor observed in previous exact numerical calculations in the chiral quark-soliton model and in chiral perturbation theory, and agrees well with the available phenomenological information. The Feynman-Hellmann theorem is used to study the pion mass dependence of the nucleon mass and a good agreement with lattice QCD results is observed. The use of the present method to extrapolate lattice data to the chiral limit is discussed.